31047951 - 3375897 - 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

Description:31047951 - 3375897 - 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p269 : Zhou, OpenPFGW
Decimal Digits:500000   (log10 is 499999.696004725)
Rank (*):3522 (digit rank is 1)
Entrance Rank (*):1326
Currently on list? (*):yes
Submitted:8/26/2015 16:21:47 CDT
Last modified:8/26/2015 22:50:30 CDT
Database id:120269
Status Flags:TrialDiv
Score (*):44.5051 (normalized score 1.3178)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Lei Zhou writes (4 Apr 2017):  (report abuse)
This is a "generalized near repdigits" prime number since its ternary representation is 2222..(672053 2s before the 1)..212..(375897 of 2s after the 1)..2.

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
fieldvalue
prime_id120269
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tp -q"3^1047951-3^375897-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 3^1047951-3^375897-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Calling Brillhart-Lehmer-Selfridge with factored part 35.87% 3^1047951-3^375897-1 is prime! (22218.1638s+0.0213s) [Elapsed time: 6.17 hours]
modified2020-07-07 17:30:17
created2015-08-26 16:31:01
id165897

Query times: 0.0007 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.